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Purpose

=======

DTRSM solves one of the matrix equations

op( A )*X = alpha*B, or X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or

non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A or op( A ) = A'.

The matrix X is overwritten on B.

Parameters

==========

SIDE - CHARACTER*1.

On entry, SIDE specifies whether op( A ) appears on the left

or right of X as follows:

SIDE = 'L' or 'l' op( A )*X = alpha*B.

SIDE = 'R' or 'r' X*op( A ) = alpha*B.

Unchanged on exit.

UPLO - CHARACTER*1.

On entry, UPLO specifies whether the matrix A is an upper or

lower triangular matrix as follows:

UPLO = 'U' or 'u' A is an upper triangular matrix.

UPLO = 'L' or 'l' A is a lower triangular matrix.

Unchanged on exit.

TRANSA - CHARACTER*1.

On entry, TRANSA specifies the form of op( A ) to be used in

the matrix multiplication as follows:

TRANSA = 'N' or 'n' op( A ) = A.

TRANSA = 'T' or 't' op( A ) = A'.

TRANSA = 'C' or 'c' op( A ) = A'.

Unchanged on exit.

DIAG - CHARACTER*1.

On entry, DIAG specifies whether or not A is unit triangular

as follows:

DIAG = 'U' or 'u' A is assumed to be unit triangular.

DIAG = 'N' or 'n' A is not assumed to be unit

triangular.

Unchanged on exit.

M - INTEGER.

On entry, M specifies the number of rows of B. M must be at

least zero.

Unchanged on exit.

N - INTEGER.

On entry, N specifies the number of columns of B. N must be

at least zero.

Unchanged on exit.

ALPHA - DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha. When alpha is

zero then A is not referenced and B need not be set before

entry.

Unchanged on exit.

A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m

when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.

Before entry with UPLO = 'U' or 'u', the leading k by k

upper triangular part of the array A must contain the upper

triangular matrix and the strictly lower triangular part of

A is not referenced.

Before entry with UPLO = 'L' or 'l', the leading k by k

lower triangular part of the array A must contain the lower

triangular matrix and the strictly upper triangular part of

A is not referenced.

Note that when DIAG = 'U' or 'u', the diagonal elements of

A are not referenced either, but are assumed to be unity.

Unchanged on exit.

LDA - INTEGER.

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program. When SIDE = 'L' or 'l' then

LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'

then LDA must be at least max( 1, n ).

Unchanged on exit.

B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).

Before entry, the leading m by n part of the array B must

contain the right-hand side matrix B, and on exit is

overwritten by the solution matrix X.

LDB - INTEGER.

On entry, LDB specifies the first dimension of B as declared

in the calling (sub) program. LDB must be at least

max( 1, m ).

Unchanged on exit.

Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.